Additive and Multiplicative Effects Models for Networks and Relational Data

Description

Analysis of network and relational data using additive and multiplicative effects (AME) models. The basic model includes regression terms, the covariance structure of the social relations model (Warner, Kenny and Stoto (1979), Wong (1982)), and multiplicative factor effects (Hoff(2009)). Four different link functions accommodate different relational data structures, including binary/network data (bin), normal relational data (nrm), ordinal relational data (ord) and data from fixed-rank nomination schemes (frn). Several of these link functions are discussed in Hoff, Fosdick, Volfovsky and Stovel (2013). Development of this software was supported in part by NICHD grant R01HD067509.

Details

Author(s)

Peter Hoff, Bailey Fosdick, Alex Volfovsky, Yanjun He

Maintainer: Peter Hoff <peter.hoff@duke.edu>

See Also

Useful links:

• https://github.com/pdhoff/amen

• Report bugs at https://github.com/pdhoff/amen/issues

Examples

data(YX_frn)
fit<-ame(YX_frn$Y,YX_frn$X,burn=5,nscan=5,odens=1,family="frn")

summary(fit)

plot(fit) 

International relations in the 90s

Description

A relational dataset recording a variety of nodal and dyadic variables on countries in the 1990s, including information on conflicts, trade and other variables. Except for the conflict variable, the variables are averages across the decade.

Format

A list consisting of a socioarray dyadvars of dyadic variables and matrix nodevars of nodal variables. The dyadic variables include

• total number of conflicts;

• exports (in billions of dollars);

• distance (in thousands of kilometers);

• number of shared IGOs (averages across the years);

• polity interaction.

The nodal variables include

• population (in millions);

• gdp (in billions of dollars);

• polity

Source

Michael Ward.

Linear combinations of submatrices of an array

Description

Computes a matrix of expected values based on an array X of predictors and a vector beta of regression coefficients.

Usage

Xbeta(X, beta)

Arguments

Value

An n by n matrix

Author(s)

Peter Hoff

binary relational data and covariates

Description

a synthetic dataset that includes binary relational data as well as information on eight covariates

Usage

data(YX_bin)

Format

The format is: List of 2 $ Y: num [1:100, 1:100] NA 0 0 0 0 0 0 0 0 1 ... $ X: num [1:100, 1:100, 1:8] 1 1 1 1 1 1 1 1 1 1 ... ..- attr(*, "dimnames")=List of 3 .. ..$ : NULL .. ..$ : NULL .. ..$ : chr [1:8] "intercept" "rgpa" "rsmoke" "cgpa" ...

Examples

data(YX_bin)
gofstats(YX_bin$Y) 

binary relational data and covariates

Description

a synthetic dataset that includes longitudinal binary relational data as well as information on covariates

Usage

data(YX_bin_long)

Format

a list

Examples

data(YX_bin_long)
gofstats(YX_bin_long$Y[,,1]) 

Censored binary nomination data and covariates

Description

a synthetic dataset that includes relational data where the number of nominations per row is censored at 10, along with information on eight covariates

Usage

data(YX_cbin)

Format

The format is: List of 2 $ Y: num [1:100, 1:100] NA 0 0 0 1 0 0 0 0 3 ... $ X: num [1:100, 1:100, 1:8] 1 1 1 1 1 1 1 1 1 1 ... ..- attr(*, "dimnames")=List of 3 .. ..$ : NULL .. ..$ : NULL .. ..$ : chr [1:8] "intercept" "rgpa" "rsmoke" "cgpa" ...

Examples

data(YX_cbin)
gofstats(YX_cbin$Y) 

Fixed rank nomination data and covariates

Description

a synthetic dataset that includes fixed rank nomination data as well as information on eight covariates

Usage

data(YX_frn)

Format

The format is: List of 2 $ Y: num [1:100, 1:100] NA 0 0 0 1 0 0 0 0 3 ... $ X: num [1:100, 1:100, 1:8] 1 1 1 1 1 1 1 1 1 1 ... ..- attr(*, "dimnames")=List of 3 .. ..$ : NULL .. ..$ : NULL .. ..$ : chr [1:8] "intercept" "rgpa" "rsmoke" "cgpa" ...

Examples

data(YX_frn)
gofstats(YX_frn$Y) 

normal relational data and covariates

Description

a synthetic dataset that includes continuous (normal) relational data as well as information on eight covariates

Usage

data(YX_nrm)

Format

The format is: List of 2 $ Y: num [1:100, 1:100] NA -4.05 -0.181 -3.053 -1.579 ... $ X: num [1:100, 1:100, 1:8] 1 1 1 1 1 1 1 1 1 1 ... ..- attr(*, "dimnames")=List of 3 .. ..$ : NULL .. ..$ : NULL .. ..$ : chr [1:8] "intercept" "rgpa" "rsmoke" "cgpa" ...

Examples

data(YX_nrm)
gofstats(YX_nrm$Y)

ordinal relational data and covariates

Description

a synthetic dataset that includes ordinal relational data as well as information on seven covariates

Usage

data(YX_ord)

Format

The format is: List of 2 $ Y: num [1:100, 1:100] NA 0 3 0 3 1 0 1 1 0 ... $ X: num [1:100, 1:100, 1:7] 1 1 1 1 1 1 1 1 1 1 ... ..- attr(*, "dimnames")=List of 3 .. ..$ : NULL .. ..$ : NULL .. ..$ : chr [1:7] "rgpa" "rsmoke" "cgpa" "csmoke" ...

Examples

data(YX_ord)
gofstats(YX_ord$Y)

row-specific ordinal relational data and covariates

Description

a synthetic dataset that includes row-specific ordinal relational data as well as information on five covariates

Usage

data(YX_rrl)

Format

The format is: List of 2 $ Y: num [1:100, 1:100] NA 0 3 0 3 1 0 1 1 0 ... $ X: num [1:100, 1:100, 1:5] 1 1 1 1 1 1 1 1 1 1 ... ..- attr(*, "dimnames")=List of 3 .. ..$ : NULL .. ..$ : NULL .. ..$ : chr [1:5] "cgpa" "csmoke" "igrade" "ismoke" ...

Examples

data(YX_rrl)
gofstats(YX_rrl$Y)

AddHealth community 3 data

Description

A valued sociomatrix (Y) and matrix of nodal attributes (X) for students in community 3 of the AddHealth study.

• Y: A sociomatrix in which the value of the edge corresponds to an ad-hoc measure of intensity of the relation. Note that students were only allowed to nominate up to 5 male friends and 5 female friends.

• X: Matrix of students attributes, including sex, race (1=white, 2=black, 3=hispanic, 4=asian, 5=mixed/other) and grade.

Usage

data(addhealthc3)

Format

list

AddHealth community 9 data

Description

A valued sociomatrix (Y) and matrix of nodal attributes (X) for students in community 9 of the AddHealth study.

• Y: A sociomatrix in which the value of the edge corresponds to an ad-hoc measure of intensity of the relation. Note that students were only allowed to nominate up to 5 male friends and 5 female friends.

• X: Matrix of students attributes, including sex, race (1=white, 2=black, 3=hispanic, 4=asian, 5=mixed/other) and grade.

Usage

data(addhealthc9)

Format

list

Add lines

Description

Add lines to a network plot

Usage

addlines(Y,X,col="lightblue",alength=0,...)

Arguments

Author(s)

Peter Hoff

Examples

data(addhealthc3) 
Y<-addhealthc3$Y
X<-xnet(Y) 
netplot(Y,X) 
addlines(Y,X,col=Y[Y!=0]) 

AME model fitting routine

Description

An MCMC routine providing a fit to an additive and multiplicative effects (AME) regression model to relational data of various types

Usage

ame(Y, Xdyad=NULL, Xrow=NULL, Xcol=NULL, family, R=0, rvar = !(family=="rrl") ,
cvar = TRUE,  dcor = !symmetric, nvar=TRUE,
intercept=!is.element(family,c("rrl","ord")),
symmetric=FALSE,
odmax=rep(max(apply(Y>0,1,sum,na.rm=TRUE)),nrow(Y)), seed = 1, nscan =
10000, burn = 500, odens = 25, plot=TRUE, print = TRUE, gof=TRUE,
prior=list())

Arguments

Details

This command provides posterior inference for parameters in AME models of relational data, assuming one of six possible data types/models:

"nrm": A normal AME model.

"tob": A tobit AME model.

"bin": A binary probit AME model.

"ord": An ordinal probit AME model. An intercept is not identifiable in this model.

"cbin": An AME model for censored binary data. The value of 'odmax' specifies the maximum number of links each row may have.

"frn": An AME model for fixed rank nomination networks. A higher value of the rank indicates a stronger relationship. The value of 'odmax' specifies the maximum number of links each row may have.

"rrl": An AME model based on the row ranks. This is appropriate if the relationships across rows are not directly comparable in terms of scale. An intercept, row random effects and row regression effects are not estimable for this model.

Value

Author(s)

Peter Hoff

Examples

data(YX_frn) 
fit<-ame(YX_frn$Y,YX_frn$X,burn=5,nscan=5,odens=1,family="frn")
# you should run the Markov chain much longer than this

 

AME model fitting routine for replicated relational data

Description

An MCMC routine providing a fit to an additive and multiplicative effects (AME) regression model to replicated relational data of various types.

Usage

ame_rep(Y,Xdyad=NULL, Xrow=NULL, Xcol=NULL, family, R=0, rvar = !(family=="rrl"),
cvar = TRUE, dcor = !symmetric, nvar=TRUE,  
intercept=!is.element(family,c("rrl","ord")),
symmetric=FALSE,
odmax=rep(max(apply(Y>0,c(1,3),sum,na.rm=TRUE)),nrow(Y[,,1])), seed = 1,
nscan = 10000, burn = 500, odens = 25, plot=TRUE, print = TRUE, gof=TRUE)

Arguments

Details

This command provides posterior inference for parameters in AME models of independent replicated relational data, assuming one of six possible data types/models:

"nrm": A normal AME model.

"bin": A binary probit AME model.

"ord": An ordinal probit AME model. An intercept is not identifiable in this model.

"cbin": An AME model for censored binary data. The value of 'odmax' specifies the maximum number of links each row may have.

"frn": An AME model for fixed rank nomination networks. A higher value of the rank indicates a stronger relationship. The value of 'odmax' specifies the maximum number of links each row may have.

"rrl": An AME model based on the row ranks. This is appropriate if the relationships across rows are not directly comparable in terms of scale. An intercept, row random effects and row regression effects are not estimable for this model.

Value

Author(s)

Peter Hoff, Yanjun He

Examples

data(YX_bin_long) 
fit<-ame_rep(YX_bin_long$Y,YX_bin_long$X,burn=5,nscan=5,odens=1,family="bin")
# you should run the Markov chain much longer than this

Circular network plot

Description

Produce a circular network plot.

Usage

circplot(
  Y,
  U = NULL,
  V = NULL,
  row.names = rownames(Y),
  col.names = colnames(Y),
  plotnames = TRUE,
  vscale = 0.8,
  pscale = 1.75,
  mscale = 0.3,
  lcol = "gray",
  rcol = "brown",
  ccol = "blue",
  pch = 16,
  lty = 3,
  jitter = 0.1 * (nrow(Y)/(1 + nrow(Y))),
  bty = "n",
  add = FALSE
)

Arguments

Details

This function creates a circle plot of a relational matrix or social network. If not supplied via U and V, two-dimensional row factors and column factors are computed from the SVD of Y, scaled versions of which are used to plot positions on the outside edge (U) and inside edge (V) of the circle plot. The magnitudes of the plotting characters are determined by the magnitudes of the rows of U and V. Segments are drawn between each row object i and column object j for which Y[i,j]!=0.

Author(s)

Peter Hoff

Examples

data(IR90s) 
circplot(IR90s$dyadvars[,,1])

Cold War data

Description

Positive and negative relations between countries during the cold war

Format

A list including the following dyadic and nodal variables:

• cc: a socioarray of ordinal levels of military cooperation (positive) and conflict (negative), every 5 years;

• distance: between-country distance (in thousands of kilometers);

• gdp: country gdp in dollars every 5 years;

• polity: country polity every 5 years.

Source

Xun Cao : https://polisci.la.psu.edu/people/xuc11/

Comtrade data

Description

Eleven years of import and export data between 229 countries. The data use the SITC Rev. 1 commodity classification, aggregated at the first level (AG1).

Format

A list consisting of a socioarray Trade and a vector dollars2010 of inflation rates. The socioarray gives yearly trade volume (exports and imports) in dollars for 10 different commodity classes for eleven years between 229 countries. This gives a five-way array. The first index is the reporting country, so Trade[i,j,t,k,1] is what i reports for exports to j, but in general this is not the same as Trade[j,i,t,k,2], what j reports as importing from i.

Source

https://comtrade.un.org, https://www.measuringworth.com

Computes the design socioarray of covariate values

Description

Computes the design socioarray of covariate values for an AME fit

Usage

design_array(Xrow=NULL,Xcol=NULL,Xdyad=NULL,intercept=TRUE,n)

Arguments

Value

an n x n x (pr+pc+pd+intercept) 3-way array

Author(s)

Peter Hoff

Dutch college data

Description

Longitudinal relational measurements and nodal characteristics of Dutch college students, described in van de Bunt, van Duijn, and Snijders (1999). The time interval between the first four measurements was three weeks, whereas the interval between the last three was six weeks.

Format

A list consisting of a socioarray Y and a matrix X of static nodal attributes. The relational measurements range from -1 to 4, indicating the following:

• -1 a troubled or negative relationship

• 0 don't know

• 1 neutral relationship

• 2 friendly

• 3 friendship

• 4 best friends

Source

Linton Freeman

Edgelist to sociomatrix

Description

Construction of a sociomatrix from an edgelist

Usage

el2sm(el,directed=TRUE,nadiag=all(el[,1]!=el[,2]))

Arguments

Value

a sociomatrix

Author(s)

Peter Hoff

Examples

Y<-matrix(rpois(10*10,.5),10,10) ; diag(Y)<-NA
E<-sm2el(Y) 
el2sm(E) - Y 

Goodness of fit statistics

Description

Goodness of fit statistics evaluating second and third-order dependence patterns

Usage

gofstats(Y)

Arguments

Value

a vector of gof statistics

Author(s)

Peter Hoff

Examples

data(YX_nrm) 

gofstats(YX_nrm$Y) 

Lazega's law firm data

Description

Several nodal and dyadic variables measured on 71 attorneys in a law firm.

Format

A list consisting of a socioarray Y and a nodal attribute matrix X.

The dyadic variables in Y include three binary networks: advice, friendship and co-worker status.

The categorical nodal attributes in X are coded as follows:

• status (1=partner, 2=associate)

• office (1=Boston, 2=Hartford, 3=Providence)

• practice (1=litigation, 2=corporate)

• law school (1=Harvard or Yale, 2=UConn, 3=other)

seniority and age are given in years, and female is a binary indicator.

Source

Linton Freeman

log density for GBME models

Description

Calculation of the log conditional density of the latent AMEN matrix Z given observed data Y.

Usage

ldZgbme(Z, Y, llYZ, EZ, rho, s2 = 1)

Arguments

Details

This function is used for updating dyadic pairs of the latent variable matrix Z based on Y and an AMEN model for Z. The function llYZ specifies the log likelihood for each single z[i,j] based on y[i,j], that is, llYZ gives the log probability density (or mass function) of y[i,j] given z[i,j].

Value

a symmetric matrix where entry i,j is proportional to the log conditional bivariate density of z[i,j],z[j,i].

Author(s)

Peter Hoff

Examples

## For (overdispersed) Poisson regression, use
llYZ<-function(y,z){ dpois(y,z,log=TRUE) } 

SRM log likelihood evaluated on a grid of rho-values

Description

Calculation of the SRM log-likelihood over a grid of rho-values

Usage

llsrmRho(Y, Sab, rhos, s2 = 1)

Arguments

Value

a vector of log-likelihood values

Author(s)

Peter Hoff

Symmetric square root of a matrix

Description

Computes the symmetric square root of a positive definite matrix

Usage

mhalf(M)

Arguments

Value

a matrix H such that H^2 equals M

Author(s)

Peter Hoff

Network plotting

Description

Plot the graph of a sociomatrix

Usage

netplot(Y,X=NULL,xaxt="n",yaxt="n",xlab="",ylab="",
 lcol="gray",ncol="black",lwd=1,lty=1,pch=16,bty="n",plotnames=FALSE,
 seed=1,
 plot.iso=TRUE,directed=NULL,add=FALSE,...)

Arguments

Author(s)

Peter Hoff

Examples

data(addhealthc3)
Y<-addhealthc3$Y
X<-xnet(Y) 
netplot(Y,X) 

Plot results of an AME object

Description

A set of plots summarizing the MCMC routine for an AME fit, as well as some posterior predictive checks.

Usage

## S3 method for class 'ame'
plot(x, ...)

Arguments

Value

a series of plots

Author(s)

Peter Hoff

Precomputation of design matrix quantities.

Description

Computation of a variety of quantities from the design array to be used in MCMC model fitting algorithms.

Usage

precomputeX(X)

Arguments

Value

the same three-way array but with derived quantities as attributes.

Author(s)

Peter Hoff

Gibbs update for additive effects covariance

Description

Gibbs update for additive effects covariance

Usage

rSab_fc(a,b,Sab0=NULL,eta0=NULL)

Arguments

Author(s)

Peter Hoff

Gibbs update for multiplicative effects covariance

Description

Gibbs update for multiplicative effects covariance

Usage

rSuv_fc(U,V, Suv0=NULL,kappa0=NULL)

Arguments

Author(s)

Peter Hoff

Gibbs sampling of U and V

Description

A Gibbs sampler for updating the multiplicative effect matrices U and V

Usage

rUV_fc(Z, U, V, Suv, rho, s2 = 1, offset = 0)

Arguments

Value

Author(s)

Peter Hoff

Gibbs sampling of U and V

Description

A Gibbs sampler for updating the multiplicative effect matrices U and V, assuming they are the same across replicates.

Usage

rUV_rep_fc(E.T,U,V,rho,s2=1,shrink=TRUE)

Arguments

Value

Author(s)

Peter Hoff, Yanjun He

Gibbs sampling of U and V

Description

A Gibbs sampler for updating the multiplicative effect matrices U and V in the symmetric case. In this case U%*%t(V) is symmetric, so this is parameterized as V=U%*%L where L is the diagonal matrix of eigenvalues of U%*%t(V).

Usage

rUV_sym_fc(E, U, V, s2 = 1, shrink=TRUE)

Arguments

Value

Author(s)

Peter Hoff

Examples

U0<-matrix(rnorm(30,2),30,2) ; V0<-U0%*%diag(c(3,-2)) 
E<- U0%*%t(V0) + matrix(rnorm(30^2),30,30) 
rUV_sym_fc 

Simulate Z based on a probit model

Description

Simulates a random latent matrix Z given its expectation, dyadic correlation and a binary relational matrix Y

Usage

rZ_bin_fc(Z, EZ, rho, Y)

Arguments

Value

a square matrix , the new value of Z

Author(s)

Peter Hoff

Simulate Z given fixed rank nomination data

Description

Simulates a random latent matrix Z given its expectation, dyadic correlation and censored binary nomination data

Usage

rZ_cbin_fc(Z, EZ, rho, Y, odmax, odobs)

Arguments

Details

simulates Z under the constraints (1) Y[i,j]=1, Y[i,k]=0 => Z[i,j]>Z[i,k] , (2) Y[i,j]=1 => Z[i,j]>0 , (3) Y[i,j]=0 & odobs[i]<odmax[i] => Z[i,j]<0

Value

a square matrix, the new value of Z

Author(s)

Peter Hoff

Simulate Z given fixed rank nomination data

Description

Simulates a random latent matrix Z given its expectation, dyadic correlation and fixed rank nomination data

Usage

rZ_frn_fc(Z, EZ, rho, Y, YL, odmax, odobs)

Arguments

Details

simulates Z under the constraints (1) Y[i,j]>Y[i,k] => Z[i,j]>Z[i,k] , (2) Y[i,j]>0 => Z[i,j]>0 , (3) Y[i,j]=0 & odobs[i]<odmax[i] => Z[i,j]<0

Value

a square matrix, the new value of Z

Author(s)

Peter Hoff

Simulate missing values in a normal AME model

Description

Simulates missing values of a sociomatrix under a normal AME model

Usage

rZ_nrm_fc(Z, EZ, rho,s2, Y)

Arguments

Value

a square matrix, equal to Y at non-missing values

Author(s)

Peter Hoff

Simulate Z given the partial ranks

Description

Simulates a random latent matrix Z given its expectation, dyadic correlation and partial rank information provided by W

Usage

rZ_ord_fc(Z, EZ, rho, Y)

Arguments

Value

a square matrix, the new value of Z

Author(s)

Peter Hoff

Simulate Z given relative rank nomination data

Description

Simulates a random latent matrix Z given its expectation, dyadic correlation and relative rank nomination data

Usage

rZ_rrl_fc(Z, EZ, rho, Y, YL)

Arguments

Details

simulates Z under the constraints (1) Y[i,j]>Y[i,k] => Z[i,j]>Z[i,k]

Value

a square matrix, the new value of Z

Author(s)

Peter Hoff

Simulate Z based on a tobit model

Description

Simulates a random latent matrix Z given its expectation, dyadic correlation and a nonnegative relational matrix Y

Usage

rZ_tob_fc(Z, EZ,rho,s2,Y)

Arguments

Value

a square matrix, the new value of Z

Author(s)

Peter Hoff

Simulate a and Sab from full conditional distributions under bin likelihood

Description

Simulate a and Sab from full conditional distributions under bin likelihood

Usage

raSab_bin_fc(Z, Y, a, b, Sab, Sab0=NULL, eta0=NULL, SS = round(sqrt(nrow(Z))))

Arguments

Value

Author(s)

Peter Hoff

Simulate a and Sab from full conditional distributions under the cbin likelihood

Description

Simulate a and Sab from full conditional distributions under the cbin likelihood

Usage

raSab_cbin_fc(Z, Y, a, b, Sab, odmax, odobs, Sab0=NULL, eta0=NULL,SS =
round(sqrt(nrow(Z))))

Arguments

Value

Author(s)

Peter Hoff

Simulate a and Sab from full conditional distributions under frn likelihood

Description

Simulate a and Sab from full conditional distributions under frn likelihood

Usage

raSab_frn_fc(Z, Y, YL, a, b, Sab, odmax, odobs, Sab0=NULL, eta0=NULL,
SS=round(sqrt(nrow(Z))))

Arguments

Value

Author(s)

Peter Hoff

Conditional simulation of additive effects and regression coefficients

Description

Simulates from the joint full conditional distribution of (beta,a,b) in a social relations regression model

Usage

rbeta_ab_fc(
  Z,
  Sab,
  rho,
  X = NULL,
  s2 = 1,
  offset = 0,
  iV0 = NULL,
  m0 = NULL,
  g = length(Z)
)

Arguments

Value

Author(s)

Peter Hoff

Gibbs sampling of additive row and column effects and regression coefficient with independent replicate relational data

Description

Simulates from the joint full conditional distribution of (a,b,beta), assuming same additive row and column effects and regression coefficient across replicates.

Usage

rbeta_ab_rep_fc(Z.T,Sab,rho,X.T,s2=1)

Arguments

Value

Author(s)

Peter Hoff, Yanjun He

Simulation from a multivariate normal distribution

Description

Simulates a matrix where the rows are i.i.d. samples from a multivariate normal distribution

Usage

rmvnorm(n, mu, Sigma, Sigma.chol = chol(Sigma))

Arguments

Value

a matrix with n rows

Author(s)

Peter Hoff

Griddy Gibbs update for dyadic correlation

Description

Simulation of dyadic correlation from its approximate full conditional distribution using griddy Gibbs sampling

Usage

rrho_fc(Z, Sab, s2 = 1, offset = 0, ngp = 100, asp = NULL)

Arguments

Value

a value of rho

Author(s)

Peter Hoff

Metropolis update for dyadic correlation

Description

Metropolis update for dyadic correlation

Usage

rrho_mh(Z, rho, s2 = 1,offset=0, asp=NULL)

Arguments

Value

a new value of rho

Author(s)

Peter Hoff

Metropolis update for dyadic correlation with independent replicate data

Description

Metropolis update for dyadic correlation with independent replicate data.

Usage

rrho_mh_rep(E.T, rho, s2 = 1)

Arguments

Value

a new value of rho

Author(s)

Peter Hoff, Yanjun He

Gibbs update for dyadic variance

Description

Gibbs update for dyadic variance

Usage

rs2_fc(Z, rho,offset=0,nu0=NULL,s20=NULL)

Arguments

Value

a new value of s2

Author(s)

Peter Hoff

Gibbs update for dyadic variance with independent replicate relational data

Description

Gibbs update for dyadic variance with independent replicate relational data

Usage

rs2_rep_fc(E.T, rho)

Arguments

Value

a new value of s2

Author(s)

Peter Hoff, Yanjun He

Simulation from a Wishart distribution

Description

Simulates a random Wishart-distributed matrix

Usage

rwish(S0, nu = dim(S0)[1] + 2)

Arguments

Value

a positive definite matrix

Author(s)

Peter Hoff

Examples

## The expectation is S0*nu

S0<-rwish(diag(3)) 

SS<-matrix(0,3,3) 
for(s in 1:1000) { SS<-SS+rwish(S0,5) }

SS/s 

S0*5

Sampson's monastery data

Description

Several dyadic variables measured on 18 members of a monastery.

Format

A socioarray whose dimensions represent nominators, nominatees and relations. Each monk was asked to rank up to three other monks on a variety of positive and negative relations. A rank of three indicates the "highest" ranking for a particular relational variable. The relations like_m2 and like_m1 are evaluations of likeing at one and two timepoints previous to when the other relations were measured.

Source

Linton Freeman

Sheep dominance data

Description

Number of dominance encounters between 28 female bighorn sheep. Cell (i,j) records the number of times sheep i dominated sheep j. From Hass (1991).

Format

A list consisting of the following:

• dom: a directed socioarray recording the number of dominance encounters.

• age: the age of each sheep in years.

Source

Linton Freeman

Simulate a network, i.e. a binary relational matrix

Description

Simulates a network, i.e. a binary relational matrix

Usage

simY_bin(EZ, rho)

Arguments

Value

a square binary matrix

Author(s)

Peter Hoff

Simulate an relational matrix based on a fixed rank nomination scheme

Description

Simulate an relational matrix based on a fixed rank nomination scheme

Usage

simY_frn(EZ, rho, odmax, YO)

Arguments

Value

a square matrix, where higher values represent stronger relationships

Author(s)

Peter Hoff

Simulate a normal relational matrix

Description

Simulates a normal relational matrix

Usage

simY_nrm(EY, rho, s2)

Arguments

Value

a square matrix

Author(s)

Peter Hoff

Simulate an ordinal relational matrix

Description

Simulates an ordinal relational matrix having a particular marginal distribution

Usage

simY_ord(EZ, rho, Y)

Arguments

Value

a square matrix

Author(s)

Peter Hoff

Simulate an relational matrix based on a relative rank nomination scheme

Description

Simulate an relational matrix based on a relative rank nomination scheme

Usage

simY_rrl(EZ, rho, odobs, YO)

Arguments

Value

a square matrix, where higher values represent stronger relationships

Author(s)

Peter Hoff

Simulate a tobit relational matrix

Description

Simulates a tobit relational matrix

Usage

simY_tob(EY, rho, s2)

Arguments

Value

a square matrix

Author(s)

Peter Hoff

Simulate Z given its expectation and covariance

Description

Simulate Z given its expectation and covariance

Usage

simZ(EZ, rho, s2 = 1)

Arguments

Value

a simulated value of Z

Author(s)

Peter Hoff

Sociomatrix to edgelist

Description

Construction of an edgelist from a sociomatrix

Usage

sm2el(sm,directed=TRUE)

Arguments

Value

an edglist

Author(s)

Peter Hoff

Examples

Y<-matrix(rpois(10*10,.5),10,10) ; diag(Y)<-NA
E<-sm2el(Y) 
el2sm(E) - Y 

Summary of an AME object

Description

Summary method for an AME object

Usage

## S3 method for class 'ame'
summary(object, ...)

Arguments

Value

a summary of parameter estimates and confidence intervals for an AME fit

Author(s)

Peter Hoff

Network embedding

Description

Compute an embedding of a sociomatrix into a two-dimensional space.

Usage

xnet(
  Y,
  fm = try(requireNamespace("network", quietly = TRUE), silent = TRUE),
  seed = 1
)

Arguments

Details

Coordinates are obtained using the Fruchterman-Reingold layout if the package network is installed, and otherwise uses the first two eigenvectors the sociomatrix.

Value

(matrix) A matrix of two-dimensional coordinates.

Author(s)

Peter Hoff

Examples

data(addhealthc3) 
Y<-addhealthc3$Y
X<-xnet(Y) 
netplot(Y,X) 

rank-based z-scores

Description

Computes the normal scores corresponding to the ranks of a data vector

Usage

zscores(y,ties.method="average")

Arguments

Value

a numeric vector

Author(s)

Peter Hoff